1. Field of the Invention
The invention relates to a half-band filter for a cellular group demultiplexer. More specifically, the invention relates to such a half-band filter denoted by the generic name splitter.
Even more specifically, the invention relates to improvements in such splitters.
In accordance with the invention, there is provided splitters which use a smaller number of multipliers than conventional splitters.
2. Description of Prior Art
The use of satellites with multiple spot beam is a major step in increasing the capabilities of satellite communication. Multiple beam satellites have the advantage of having high gain and allowing the reuse of the same frequency band in geographically separated beams. The use of multiple spot beams will require additional switching on-board the satellite. This switching can be done either in the RF, IF or the baseband. Switching at the RF and IF will necessitate the use of Time Division Multiple Access (TDMA) in the uplink which could lead to high rate modems in the earth stations. This could increase the cost of earth stations. On-board switching in the baseband requires down-conversion, demultiplexing and demodulation of the uplink data prior to switching and re-multiplexing, remodulation and upconversion after switching to form the downlink. The part of the signal processing in the baseband is called On-board Baseband Processing (OBP). The use of the OBP results in a considerable flexibility in the choice of the access scheme and either TDMA or Frequency Division Multiple Access (FDMA) can be used. For the payloads with OBP, the use of FDMA is considered on the uplink to reduce ground station cost. On the other hand, Time Division Multiplexing (TDM) is used for its power efficiency on the downlink.
Use of FDMA on the uplink will reduce the size of the earth terminal as compared to TDMA. However, the price paid is the increased complexity of the spacecraft payload. While a single demodulator is sufficient for demodulation of high bit rate TDMA on the uplink, several demodulators are required for the demodulation of the FDMA carriers received by the satellite. A solution to this problem is the use of a multi-carrier demodulator, referred to as a group demultiplexer/demodulator. The more important and computational intensive section, referred to as the group demultiplexer, divides the incoming composite spectrum into separate channels. The second section, the demodulator, recovers the digital data for each individual channel.
There are several techniques for the group demultiplexer design. A straightforward method is per-channel filtering. In this method, a separate filter is used for each channel. This is only feasible for a small number of channels. For a large number of channels sharp filters with many taps are required. Another method is the FFT/IFFT or, frequency-domain filtering. In this method, a Fast Fourier Transform (FFT) is used to find the frequency spectrum of the composite FDM signal. Following the FFT, the frequency-domain coefficients are multiplied by coefficients of a filter in order to determine the frequency-domain samples falling into each of the carrier channels. For each set of frequency-domain coefficients, an Inverse FFT (IFFT) is used to recover the time-domain samples of the modulated carriers. This method is much less complex than the per-channel approach, while having a great degree of flexibility.
Another method for the implementation of the group demultiplexer is the polyphase/FFT method. In this method, a digital filter bank is implemented in cascade with an FFT processor. This technique can be used when the bandwidths of the channels are equal and fixed. There is another technique, called tree or multistage group demultiplexer. In the tree group demultiplexer technique, a set of filters is arranged in a tree structure (usually a binary tree). The number of channels demultiplexed by the binary tree is a power of 2 (a power of q if q-ary tree is used). The demultiplexer makes use of filters to split the number of channels into two (q in general) at each node of the tree. After successive stages of filtering and decimation, the channels are demultiplexed. An important property of the multistage demultiplexer is its modularity, due to the fact that the filters are replicated in each stage. With this demultiplexer, it is possible to obtain, from the intermediate stages, channels with wider bandwidths. Recently, several authors have introduced different architectures for the tree demultiplexer. However, for the most part, these different structures constitute the description of the same principles in different ways.
In this application a new structure for the demultiplexer based on the time multiplexing of a unique single cell is introduced. This structure, while using the idea of a two way channelizer, is different in many respects from previously proposed schemes. In this section, we present the basics of the new cellular demultiplexer. The group demultiplexer is intended to transform a single input consisting of N frequency multiplexed signals into N time signals at its output, each corresponding to one of the components of the input signal. The proposed group demultiplexer does this in several stages. In each stage the number of channels at the output is twice the number of channels at the input, while the bandwidth of each channel is half that of the individual input channels. Because of this binary splitting of the channels, it is convenient to assume that the number of channels N is a power of 2, i.e., N=2.sup.L. The number of stages required for the demultiplexing of N channels will, therefore, be log.sub.2 N=L. Furthermore, we assume that all the channels have the same data rate or, equivalently, they occupy the same bandwidth. As we will see later, in spite of this assumption, the proposed system can be used in multirate applications.
The building block of the new demultiplexer is what we denote by the generic name splitter. Such splitters are illustrated in for example, U.S. Pat. No. 4,792,943, Gockler, Dec. 20, 1988, U.S. Pat. No. 4,839,889, Gockler, Jun. 13, 1989 and Digital TDM-FDM translator with multistage structure, IEEE Transactions on Communications, Vol. COM-26, No. 5, May 1978, pp. 734-741, Tsuda et al.
As seen in these references, a splitter is any device capable of splitting a baseband signal occupying a bandwidth W into two baseband signals each having a bandwidth of W/2. There are several different ways for implementing the splitter. For example, a splitter can be implemented using a lowpass and a bandpass filter each having a bandwidth of W/2, using a mixer and two identical lowpass filters, or using half-band filters. A multistage architecture discussed in the literature is the tree structured demultiplexer. Using the demultiplexed splitters, however, makes a system different from the tree structured demultiplexer. In the tree structured demultiplexer, the number of half-band filters in each stage is twice that of the preceding stage, while the bandwidth of each filter is one half that of those in the previous stage. On the other hand, in a system using time multiplexed splitters there is only one splitter in each stage. Furthermore, the splitters in all stages are the same, i.e., they are designed to split a signal with a bandwidth equal to the total bandwidth of all N signals into two signals each with half the total bandwidth.
In such a system, the splitter of the first stage has an input with bandwidth of W and two outputs each with bandwidth of W/2. These outputs are applied to the second stage and the second stage splits each of the inputs to form four signals each having bandwidth of W/4. In the same way, each stage doubles the number of input signals and reduces the bandwidth of each signal to one half. Finally stage L has 2.sup.L signals at the output each with bandwidth of W/2.sup.L.
The intuitive reasoning behind the present scheme is that: if a device can split a signal with bandwidth W into two signals each having a bandwidth of W/2, then it should be possible to use it in order to split two signals each with a bandwidth of W/2 into four signals each with a bandwidth of W/4, or to split four signals of W/4 bandwidth into eight signals each with a bandwidth of W/8, etc. The theoretical justification for the new scheme is based on two well-known theorems in digital signal processing, viz., the sampling theorem and the uncertainly or scale change theorem. The sampling theorem states that the number of samples per second required for the perfect reconstruction of a given signal is twice the bandwidth of the signal. In the example of multistage demultiplexer, according to the sampling theorem, the number of samples per unit of time required for each signal at the output of a given stage is half the number of samples required for the input signals of the same stage. In other words, the time interval between samples of each of the output signals is twice that of the time interval between the input samples. Compressing each output signal by reducing the time interval between the samples reduces the time duration of each output signal into one half and, therefore, according to scale change theorem, doubles its bandwidth.
According to the above discussion by proper interfacing of the splitters in different stages, we can conserve the bandwidth and the time frame. That is, the rate at which data is presented to each splitter and, therefore, the processing rate of the splitter, remains constant from stage to stage and is uniformly divided between different inputs. The procedure is equivalent to the time sharing of a high speed processor by several low speed applications.
In deriving the above structure, the splitter has been defined only in terms of the function it performs. That is, assumptions were not made about the way the splitter is implemented. Several options were mentioned earlier for the implementation of the splitter. Among those options, the most practical is sampling at twice the Nyquist rate and using half-band filters, Tsuda et al. Since the demultiplexer cell of the preferred embodiment essentially consists of a half-band filter, the terms "demultiplexer cell" and "half-band filter" are generally used synonymously throughout the present specification to describe one type of splitter. This simplifies the filter design due to the widening of the transition band. The fact that the even coefficients of the half-band filter are zero compensates for the doubling of the sampling rate. Half-band filters are characterized by a frequency response that is symmetric around .function..sub.s /4, where .function..sub.s is the sampling frequency. At this point the magnitude is half the passband magnitude.